Language and Use of Statistics

NZ Level 6 (NZC) Level 1 (NCEA)

Sampling Techniques

Lesson

The most important thing when taking a sample is that it is *representative* of the population. In other words, we want to make sure there is no bias that may affect our results. There are different ways to collect a sample. We'll go through some of them now.

An example of random sampling is numbers being drawn out in the lottery. Every number has an equal probability of being chosen.Each individual is chosen at random (by chance). In other words, each individual has the same probability of being chosen.

Think of a pack of jelly beans. There are lots of different colours in the pack aren't there? Instead of considering them as a whole group of jellybeans, we could divide them up by colour into subgroups.

Stratification is the process of dividing a group into subgroups with the same characteristics before we draw our random sample. Then we look at the size of each subgroup as a fraction of the total population. The number of items from each subgroup that are included in the sample should be in the same ratio as the amount they represent of the total population.

For example, say we decide to survey $50$50 students to find out what types of music the students at our high school liked best. It is likely that Year $7$7 students may have a different taste in music to Year $12$12 students.

Here is a list of how many students are in each year and how we would calculate the number of students from each year we would need to survey to create a stratified sample:

School Year | Number of Students | Proportional Number for Sample |
---|---|---|

$7$7 | $200$200 | $\frac{200}{1000}\times50=10$2001000×50=10 |

$8$8 | $180$180 | $\frac{180}{1000}\times50=9$1801000×50=9 |

$9$9 | $200$200 | $\frac{200}{1000}\times50=10$2001000×50=10 |

$10$10 | $140$140 | $\frac{140}{1000}\times50=7$1401000×50=7 |

$11$11 | $100$100 | $\frac{100}{1000}\times50=5$1001000×50=5 |

$12$12 | $180$180 | $\frac{180}{1000}\times50=9$1801000×50=9 |

Total |
$1000$1000 | $50$50 |

Remember!

No individual should fit into more than one subgroup, and no group of the total population should be excluded.

If we use systematic sampling, we are basically picking one in every $n$`n`^{th} item. From the sample, a starting point is chosen at random, and items are chosen at regular intervals. For example, we may choose every fifth name from a list or call every tenth business in the phone book.

Drawing out the winning ticket number in a lottery is an example of:

Random Sampling

AStratified Sampling

BSystematic Sampling

CRandom Sampling

AStratified Sampling

BSystematic Sampling

C

Choosing every $5$5th person on the class roll to take part in a survey is an example of:

Stratified Sampling

ARandom Sampling

BSystematic Sampling

CStratified Sampling

ARandom Sampling

BSystematic Sampling

C

Out of $2160$2160 students in a school, $216$216 were chosen at random and asked their favourite colour out of red, blue and yellow with $99$99 choosing red, $63$63 blue and $54$54 yellow.

One in every how many students at the school was sampled?

Estimate the total number of students in the whole school who prefer the colour red.

Estimate the total number of students in the whole school who prefer the colour blue.

Estimate the total number of students in the whole school who prefer the colour yellow.

Even though we may not get it perfectly right, we always aim to make our sample to be *representative* of the wider population as possible. This way we can draw conclusions and make sensible decisions for that population. Take some time now to investigate sampling techniques further.

Plan and conduct investigations using the statistical enquiry cycle: A justifying the variables and measures used B managing sources of variation, including through the use of random sampling C identifying and communicating features in context (trends, relationships between variables, and differences within and between distributions), using multiple displays D making informal inferences about populations from sample data E justifying findings, using displays and measures.

Investigate a given multivariate data set using the statistical enquiry cycle